https://file.aiquickdraw.com/mathbot/file/1726565877832osjk0ngl.jpg

Let's go through the problems shown in the image:

### PART 4: Absolute Value

#### 1. Evaluate the following absolute value expressions:
   - **a. |5 − 8|**
     \[
     |5 − 8| = |-3| = 3
     \]
   - **b. |12 + (−4)|**
     \[
     |12 + (−4)| = |12 − 4| = |8| = 8
     \]
   - **c. |−7| + |3|**
     \[
     |-7| + |3| = 7 + 3 = 10
     \]
   - **d. |10 − 15| + |3 − 7|**
     \[
     |10 − 15| + |3 − 7| = |-5| + |-4| = 5 + 4 = 9
     \]
   - **e. |−25 + 10|**
     \[
     |-25 + 10| = |-15| = 15
     \]

#### 2. Simplify and evaluate these combinations of absolute values:
   - **a. |2| + |−6| − |4 − 9|**
     \[
     |2| + |-6| − |4 − 9| = 2 + 6 − |-5| = 2 + 6 − 5 = 3
     \]
   - **b. |7 − 13| + |20 − 15|**
     \[
     |7 − 13| + |20 − 15| = |-6| + |5| = 6 + 5 = 11
     \]
   - **c. |18 − 25| + |(−3) + 4|**
     \[
     |18 − 25| + |-3 + 4| = |-7| + |1| = 7 + 1 = 8
     \]
   - **d. |−15 + 6| + |9 − 5|**
     \[
     |-15 + 6| + |9 − 5| = |-9| + |4| = 9 + 4 = 13
     \]
   - **e. |25 − 30| + |−10|**
     \[
     |25 − 30| + |-10| = |-5| + 10 = 5 + 10 = 15
     \]

---

### PART 5: Radicals

#### 1. Simplify the following square roots:
   - **a. \(\sqrt{50}\)**
     \[
     \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}
     \]
   - **b. \(\sqrt{72}\)**
     \[
     \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}
     \]
   - **c. \(\sqrt{32}\)**
     \[
     \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}
     \]
   - **d. \(\sqrt{75}\)**
     \[
     \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}
     \]

#### 2. Add or subtract the radicals:
   - **a. \(3\sqrt{2} + 5\sqrt{2}\)**
     \[
     3\sqrt{2} + 5\sqrt{2} = (3 + 5)\sqrt{2} = 8\sqrt{2}
     \]
   - **b. \(4\sqrt{3} − \sqrt{3}\)**
     \[
     4\sqrt{3} − \sqrt{3} = (4 − 1)\sqrt{3} = 3\sqrt{3}
     \]
   - **c. \(\sqrt{18} + 2\sqrt{2}\)**
     \[
     \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
     \]
     So, \(3\sqrt{2} + 2\sqrt{2} = (3 + 2)\sqrt{2} = 5\sqrt{2}\)
   - **d. \(5\sqrt{7} − 2\sqrt{7}\)**
     \[
     5\sqrt{7} − 2\sqrt{7} = (5 − 2)\sqrt{7} = 3\sqrt{7}
     \]

---

Do you need further clarifications or any additional details?

Here are five related questions for practice:
1. What is the absolute value of \(|-16|\)?
2. Simplify \(\sqrt{200}\).
3. How would you add \(\sqrt{18} + \sqrt{50}\)?
4. What is the result of \( |3 - 9| + |12 - 20| \)?
5. Simplify \(\sqrt{45} + \sqrt{80}\).

**Tip:** When adding or subtracting radicals, make sure the radicals have the same root value (like terms) to combine them easily.

Evaluate absolute value expressions and simplify square roots.

Learn how to evaluate absolute value expressions and simplify radicals. This guide includes step-by-step solutions for combining absolute values and simplifying square roots. Suitable for students in Grades 8-10.

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